You're doing more than some do in that situation. Having the willpower to force yourself to do things when you feel like doing absolutely nothing is the first step in pulling yourself out - Because otherwise you just sit around and brood.
Walking is a good thinking activity, and thinking is pretty important when you're down. You need to figure things out in your head before you feel comfortable with it, which may be uncomfortable, but it's probably the best thing you can do. Typically, if you can home in on the reason you feel or act a certain way, it's a lot easier to get to the root of the problem, but a lot of times those roots aren't things we want to think about, so we subconsciously bury them beneath loads of worry, which only makes things worse. You have to dig up some truths about yourself you may not be comfortable with.
Now, when I talk about 'figuring things out', I don't mean acknowledging that you feel like crud and you're dealing with a family breakup from the worst possible standpoint - That's a given. If you want to really figure things out, you need to find out what's driving your emotions, who's behind it, and why they hurt so badly. You'll be learning about yourself, and uncovering fears and worries your subconscious rather pretend don't exist. Be honest and fair to yourself. It's not a comfortable process, but it'll help, and you'll make yourself much easier to be around.
Once you've found the exact things that are eating at you, figure out which ones you can reasonably do something about. You're not going to be able to change a lot of things about the world, so it's better to focus on the ones you can change, even if there doesn't seem to be too many.
Equally important is finding something to fill your life with. It doesn't have to be equal to or superior to what you had before, but it has to be something worth living for. You know yourself better than I do, but focus on something creative and productive you enjoy or think you might enjoy and make an effort to devote at least an hour a day to it. Pick up drawing, writing, sculpting, music, some medium that you can express yourself in and make yourself good at it. If you already do one of those things, then focus on expressing your emotions, negative and positive, into it. It'll make the experience a lot more rewarding.
You'll find a way to cope eventually, but you can actively make an effort to figure things quickly and get some personal closure. You can't change the world, but you can change yourself.
I hope that helps a little bit - You may have already done all of this. If that's the case, it's just a matter of time, and things will sort themselves out.